31. Reconsider the situation described in Example 12.5, in which x  CO2 concentration and y  mass of 11-month-old pine trees. Suppose the simple linear regression model is valid for x between 450 and 750, and that b1  .008 and s  .5. Consider an experiment in which n  7, and the x values at which observations are made are x1  450, x2  500, x3 

550, x4  600, x5  650, x6  700, and x7  750.

a. Calculate , the standard deviation of .

b. What is the probability that the estimated slope based on such observations will be between .006 and .010?

c. Suppose it is also possible to make a single observation at each of the n  11 values 525, 540, 555, 570, . . . , 675. If a major objective is to estimate b1 as accurately as possible, would the experiment with n  11 be preferable to the one with n  7?